Pith Number

pith:4DBBKQ23

pith:2012:4DBBKQ23NKLP4AU2GFNJ73GMXT

not attested not anchored not stored refs pending

Gap Universality of Generalized Wigner and beta-Ensembles

Horng-Tzer Yau, Laszlo Erdos

arxiv:1211.3786 v5 · 2012-11-16 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4DBBKQ23NKLP4AU2GFNJ73GMXT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T02:51:42.527843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0c215435b6a96fe029a315a9fecccbcd58155767400607af908dd3832067d8e

Aliases

arxiv: 1211.3786 · arxiv_version: 1211.3786v5 · doi: 10.48550/arxiv.1211.3786 · pith_short_12: 4DBBKQ23NKLP · pith_short_16: 4DBBKQ23NKLP4AU2 · pith_short_8: 4DBBKQ23

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4DBBKQ23NKLP4AU2GFNJ73GMXT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e0c215435b6a96fe029a315a9fecccbcd58155767400607af908dd3832067d8e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76ebeadb9c73c02d8d495938d36bb4fce59113fb966565bd6feb8cb80d9c9d66",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-16T01:44:19Z",
    "title_canon_sha256": "dac430b44ac76024ad7fbde91bd2b8d11dd57e74cc27b6e4dd4457175e52f9f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3786",
    "kind": "arxiv",
    "version": 5
  }
}